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Continuous-time mean-variance portfolio selection with liability and regime switching

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  • Xie, Shuxiang

Abstract

A continuous-time mean-variance model for individual investors with stochastic liability in a Markovian regime switching financial market, is investigated as a generalization of the model of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466-1482]. We assume that the risky stock's price is governed by a Markovian regime-switching geometric Brownian motion, and the liability follows a Markovian regime-switching Brownian motion with drift, respectively. The evolution of appreciation rates, volatility rates and the interest rates are modulated by the Markov chain, and the Markov switching diffusion is assumed to be independent of the underlying Brownian motion. The correlation between the risky asset and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. Using the Lagrange multiplier technique and the linear-quadratic control technique, we get the expressions of the optimal portfolio and the mean-variance efficient frontier in closed forms. Further, the results of our special case without liability is consistent with those results of Zhou and Yin [Zhou, X.Y., Yin, G., 2003. Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim. 42 (4), 1466-1482].

Suggested Citation

  • Xie, Shuxiang, 2009. "Continuous-time mean-variance portfolio selection with liability and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 148-155, August.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:148-155
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    3. Yao, Haixiang & Li, Zhongfei & Chen, Shumin, 2014. "Continuous-time mean–variance portfolio selection with only risky assets," Economic Modelling, Elsevier, vol. 36(C), pages 244-251.
    4. Jun Yu, 2014. "Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 317-330, November.
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    6. Huiling Wu, 2013. "Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 918-934, September.
    7. Chanjuan Li & Zhongfei Li & Ke Fu & Haiqing Song, 2013. "Time-consistent Optimal Portfolio Strategy for Asset-liability Management under Mean-variance Criterion," Accounting and Finance Research, Sciedu Press, vol. 2(2), pages 1-89, May.
    8. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Non-homogeneous stochastic LQ control with regime switching and random coefficients," Papers 2201.01433, arXiv.org, revised Jul 2023.
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